Method for determining parameters of a unit cell of a crystal structure using diffraction

ABSTRACT

A method for determining the parameters of a unit cell of a crystal structure using diffraction is presented. The method includes the steps of repeatedly rotating the crystal at a predetermined angle, while the crystal moves in relation to a detection surface and measuring the position of radiation reflected from the crystal. The resulting combined measurements are utilized to accurately determine the unit cell dimension and orientation of the crystal.

FIELD OF THE INVENTION

The invention relates to a method of determining parameters of a unitcell of a crystal structure, in particular the dimensions andorientation of a unit cell, using diffraction, comprising the followingsteps: a. directing X- or neutron rays at a crystal rotating over apredetermined angle; b. detection of the radiation reflected by thecrystal on a two-dimensional detection surface; c. determining theposition where the reflected radiation falls on the detection surface.

BACKGROUND OF THE INVENTION

Such a method is known from practice. In the known method thereflections of the beams directed at the crystal are detected on aposition-sensitive detector, for example, a photo-sensitive plate, andon the basis of these positions which are processed further, the cellparameters of the crystal structure are determined in order to explainthe respective reflection positions on the detection surface. Accordingto the prior art the crystal is repeatedly rotated over an angle of, forexample, 1 or 2°. As a result, the cell parameter of the crystalstructure determined by this prior art technique is cursed withrelatively large inaccuracies. The position of the reflections in thetwo directions of the detector surface is indeed determined accurately;however, the position of the crystal has an uncertainty amounting toseveral tenths of degrees. The unit cells composing the crystalstructure will then exhibit deviations of several hundredth to one tenthdegree or even more, with respect to the corners that aredistinguishable in the unit cells. This accuracy can be improved bylimiting the rotation of the crystal during measuring to approximately0.1 or 0.2°, however, the number of measurements required then increasescorrespondingly.

It is the object of the invention to provide a method for determiningthe parameters of a unit cell of a crystal structure that can beperformed quickly and requires little measuring time.

To this end the method of determining parameters of a unit cell of acrystal structure using diffraction according to the invention ischaracterized in that the steps a, b and c are repeated, wherein in stepa the crystal always rotates over the same angle, that in the firstperformance of the steps a, b and c the relative movement of the crystalin relation to the detection surface is determined by only the rotationof the crystal, that in a repeat-performance of the steps a, b and c therelative movement of the crystal in relation to the detection surface isdetermined by a rotation of the crystal identical to that of the firstperformance of the steps a, b and c, and by a further relative movementof the crystal in relation to the detection surface coupled thereto, andthat the combination of the positions determined in the repeatperformance of steps c determines the angle position of the crystal inrelation to a reference value in which reflection of the beams occurs.

The idea of the invention is based on the intelligence that whenperforming repeat-measurements, the position of the reflections on thedetection surface in relation to the previous measurement can only beinfluenced by the additional relative movement of the crystal inrelation to the detection surface. Because the relative movement of thecrystal in relation to the detection surface is known and added to therotation of the crystal which is also known, it is possible by means ofgenerally known techniques to determine the position of the crystalwhereby the reflections have occurred. This position of the crystal,together with the position of the reflections on the detection surface,provides sufficient information to derive more accurately than with theprior art, the unit cell parameters that determine the crystalstructure. Further details about the determination of the crystalstructure may be left aside, as the person skilled in the art will bequite familiar with these.

Various embodiments of the method according to the invention areconceivable. A first embodiment of the method according to the inventionis characterized in that in the first performance of the steps a, b andc the crystal rotates over a first predetermined angle, and that in therepeat-performance of the steps a, b and c the crystal rotates over thefirst predetermined angle and the detection surface is moved.

It is desirable that in the repeat-performance of the steps a, b and cthe crystal rotate over a first predetermined angle and the detectionsurface be rotated over a second predetermined angle. This mayconveniently be performed in existing diffraction devices such asmarketed, for example, by Nonius B. V. at Delft.

A second embodiment of the method according to the invention ischaracterized in that in the first performance of the steps a, b and cthe crystal rotates over the first predetermined angle, and that in therepeat-performance of the steps a, b and c the crystal rotates over thefirst predetermined angle while in addition undergoing a movementsuperposed on this rotation.

It is desirable that the superposed movement of the crystal be arotation in a plane cutting the rotation plane in which the firstpredetermined angle lies. This method may also be performed verysuitably using existing diffraction devices as marketed by Nonius B. V.at Delft.

The method according to the invention further differs from the prior artin so far that during measurement the first predetermined rotation angleof the crystal is approximately 20° or more. By performing themeasurements with such a relatively large angular displacement it ispossible to obtain all the necessary information for the determinationof the parameter of a unit cell of the crystal structure, even of verysmall unit cells, with just two successive measurements. By suitablychoosing the additional relative movement of the detection surface inrelation to the crystal it is moreover possible to render the methodaccording to the invention sufficiently accurate. If in order to obtainthis additional relative movement the detection surface is, forinstance, rotated, the second predetermined angle may be adjusted toapproximately 10°. Such an angle displacement is also useful if theadditional movement is carried out by the crystal.

DETAILED DESCRIPTION OF THE INVENTION

The invention will now be explained in more detail with reference to thedrawing, which in FIG. 1 shows schematically the method of determining acrystal structure according to the prior art; and in FIG. 2 shows themethod of determining a crystal structure according to the invention ina preferred embodiment.

Those parts in the Figures that are the same are indicated by identicalreference numbers.

In the FIGS. 1 and 2 reference number 1 indicates the crystal whosestructure and thus the parameters of a unit cell, are to be determined.A beam, for example, an X-ray beam 2, is directed at the crystal whilethe crystal 1 is simultaneously rotated over a predetermined angle. Thisis indicated in the FIGS. 1 and 2 by the elliptical rotation symbolcarrying reference φ. During the rotation over an angle φ the X-rays 2are reflected by the crystal 1, projecting reflection images 3, 4 and 5on the detection surface 6. Instead of X-ray beams it is also possibleto use other suitable beams such as neutron beams. The detection surface6 may, for example, be a CCD camera that is part of a device formeasuring X-ray diffraction. Finally, based on the position of the imagepoints 3, 4 and 5 and others on the detection surface 6, the unit cellparameters of a crystal 1 are determined.

According to the invention, after carrying out the method as explainedabove with reference to FIG. 1 and whereby the image points 3, 4 and 5are formed, a repeat-measurement is performed, wherein again X-rays 2are directed at the crystal 1, and the reflected X-ray beams aredetected on the detection surface 6, to determine the image positionsthen formed on the detection surface 6. During this repeat-performanceof the measurement the crystal 1 is rotated over an identical angle φ,but in addition to this movement of the crystal 1 in relation to thedetection surface 6, the crystal 1 performs another relative movement inrelation to the detection surface 6, which movement in this preferredembodiment is a second rotation of the crystal 1 over an angle χ (seeFIG. 2) in a plane cutting the rotation plane of the crystal in whichlies the first predetermined angle φ. From the combination of thepositions of image points 3, 4 and 5 determined in the first measurementwith the image points 3′, 4′ and 5′ from the repeat-measurement, it ispossible to accurately determine the position or positions of thecrystal 1 in which the reflections of the X-rays 2 have occurred. Thesepositions of the crystal together with the previously-mentioned positionof the image points suffice to accurately determine the unit celldimensions and the orientation of the crystal.

The above description of an embodiment merely serves to explain theappended claims, without in any way limiting their protective scope.

What is claimed is:
 1. A method of determining parameters of a unit cellof a crystal structure using diffraction, comprising the followingsteps: a. directing X- or neutron rays at a crystal rotating over apredetermined angle; b. detection of the radiation reflected by thecrystal on a two-dimensional detection surface; c. determining theposition where the reflected radiation falls on the detection surface,characterized in that the steps a, b and c are repeated, wherein in stepa the crystal rotates always over the same angle, that in the firstperformance of the steps a, b and c the relative movement of the crystalin relation to the detection surface is determined by only the rotationof the crystal, that in a repeat-performance of the steps a, b and c therelative movement of the crystal in relation to the detection surface isdetermined by a rotation of the crystal identical to that of the firstperformance of the steps a, b and c, and by a further relative movementof the crystal in relation to the detection surface coupled thereto, andthat the combination of the positions determined in the repeatperformance of steps c determines the angle position of the crystal inrelation to a reference value in which reflection of the beams occurs.2. A method according to claim 1, characterized in that in the firstperformance of the steps a, b and c the crystal rotates over a firstpredetermined angle, and that in the repeat-performance of the steps a,b and c the crystal rotates over the first predetermined angle and thedetection surface is moved.
 3. A method according to claim 2,characterized in that in the repeat-performance of the steps a, b and cthe crystal rotates over the first predetermined angle and the detectionsurface rotates over a second predetermined angle.
 4. A method accordingto claim 1, characterized in that in the first performance of the stepsa, b and c the crystal rotates over the first predetermined angle, andthat in the repeat-performance of the steps a, b and c the crystalrotates over the first predetermined angle while in addition undergoinga movement superposed on this rotation.
 5. A method according to claim4, characterized in that the superposed uniform movement of the crystalis a rotation in a plane cutting the rotation plane in which the firstpredetermined angle lies.
 6. A method according to claim 1,characterized in that the first predetermined angle of rotation of thecrystal is at least approximately 20°.
 7. A method according to claim 3,characterized in that the second predetermined angle of rotation of thedetection surface of the crystal is approximately 10°.